LMFDB - Embedded newform 3185.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3185,2,Mod(1,3185)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3185, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3185.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3185 = 5 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3185.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$25.4323530438$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	3185.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.00000 q^{5} -3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.00000 q^{5} -3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} +2.41421 q^{10} +3.41421 q^{11} +5.41421 q^{12} +1.00000 q^{13} -1.41421 q^{15} +3.00000 q^{16} -0.828427 q^{17} +2.41421 q^{18} -0.585786 q^{19} -3.82843 q^{20} -8.24264 q^{22} +1.41421 q^{23} -6.24264 q^{24} +1.00000 q^{25} -2.41421 q^{26} -5.65685 q^{27} -5.65685 q^{29} +3.41421 q^{30} -1.75736 q^{31} +1.58579 q^{32} +4.82843 q^{33} +2.00000 q^{34} -3.82843 q^{36} -8.48528 q^{37} +1.41421 q^{38} +1.41421 q^{39} +4.41421 q^{40} +3.17157 q^{41} -11.0711 q^{43} +13.0711 q^{44} +1.00000 q^{45} -3.41421 q^{46} +4.82843 q^{47} +4.24264 q^{48} -2.41421 q^{50} -1.17157 q^{51} +3.82843 q^{52} +2.48528 q^{53} +13.6569 q^{54} -3.41421 q^{55} -0.828427 q^{57} +13.6569 q^{58} -1.75736 q^{59} -5.41421 q^{60} +8.00000 q^{61} +4.24264 q^{62} -9.82843 q^{64} -1.00000 q^{65} -11.6569 q^{66} -2.00000 q^{67} -3.17157 q^{68} +2.00000 q^{69} +11.8995 q^{71} +4.41421 q^{72} -8.48528 q^{73} +20.4853 q^{74} +1.41421 q^{75} -2.24264 q^{76} -3.41421 q^{78} -8.48528 q^{79} -3.00000 q^{80} -5.00000 q^{81} -7.65685 q^{82} +3.17157 q^{83} +0.828427 q^{85} +26.7279 q^{86} -8.00000 q^{87} -15.0711 q^{88} -6.00000 q^{89} -2.41421 q^{90} +5.41421 q^{92} -2.48528 q^{93} -11.6569 q^{94} +0.585786 q^{95} +2.24264 q^{96} +7.65685 q^{97} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 - 6 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} + 8 q^{12} + 2 q^{13} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} - 8 q^{22} - 4 q^{24} + 2 q^{25} - 2 q^{26} + 4 q^{30} - 12 q^{31} + 6 q^{32} + 4 q^{33} + 4 q^{34} - 2 q^{36} + 6 q^{40} + 12 q^{41} - 8 q^{43} + 12 q^{44} + 2 q^{45} - 4 q^{46} + 4 q^{47} - 2 q^{50} - 8 q^{51} + 2 q^{52} - 12 q^{53} + 16 q^{54} - 4 q^{55} + 4 q^{57} + 16 q^{58} - 12 q^{59} - 8 q^{60} + 16 q^{61} - 14 q^{64} - 2 q^{65} - 12 q^{66} - 4 q^{67} - 12 q^{68} + 4 q^{69} + 4 q^{71} + 6 q^{72} + 24 q^{74} + 4 q^{76} - 4 q^{78} - 6 q^{80} - 10 q^{81} - 4 q^{82} + 12 q^{83} - 4 q^{85} + 28 q^{86} - 16 q^{87} - 16 q^{88} - 12 q^{89} - 2 q^{90} + 8 q^{92} + 12 q^{93} - 12 q^{94} + 4 q^{95} - 4 q^{96} + 4 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 - 6 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^11 + 8 * q^12 + 2 * q^13 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 - 8 * q^22 - 4 * q^24 + 2 * q^25 - 2 * q^26 + 4 * q^30 - 12 * q^31 + 6 * q^32 + 4 * q^33 + 4 * q^34 - 2 * q^36 + 6 * q^40 + 12 * q^41 - 8 * q^43 + 12 * q^44 + 2 * q^45 - 4 * q^46 + 4 * q^47 - 2 * q^50 - 8 * q^51 + 2 * q^52 - 12 * q^53 + 16 * q^54 - 4 * q^55 + 4 * q^57 + 16 * q^58 - 12 * q^59 - 8 * q^60 + 16 * q^61 - 14 * q^64 - 2 * q^65 - 12 * q^66 - 4 * q^67 - 12 * q^68 + 4 * q^69 + 4 * q^71 + 6 * q^72 + 24 * q^74 + 4 * q^76 - 4 * q^78 - 6 * q^80 - 10 * q^81 - 4 * q^82 + 12 * q^83 - 4 * q^85 + 28 * q^86 - 16 * q^87 - 16 * q^88 - 12 * q^89 - 2 * q^90 + 8 * q^92 + 12 * q^93 - 12 * q^94 + 4 * q^95 - 4 * q^96 + 4 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.41421	−1.70711	−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421	−1.70711	−0.853553	+	0.521005i	$0.825557\pi$
$3$	1.41421	0.816497	0.408248	−	0.912871i	$-0.366140\pi$
$3$	1.41421	0.816497	0.408248	+	0.912871i	$0.366140\pi$
$4$	3.82843	1.91421
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.41421	−1.39385
$7$	0	0
$7$	0	0
$8$	−4.41421	−1.56066
$9$	−1.00000	−0.333333
$10$	2.41421	0.763441
$11$	3.41421	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$11$	3.41421	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$12$	5.41421	1.56295
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−1.41421	−0.365148
$16$	3.00000	0.750000
$17$	−0.828427	−0.200923	−0.100462	−	0.994941i	$-0.532032\pi$
$17$	−0.828427	−0.200923	−0.100462	+	0.994941i	$0.532032\pi$
$18$	2.41421	0.569036
$19$	−0.585786	−0.134389	−0.0671943	−	0.997740i	$-0.521405\pi$
$19$	−0.585786	−0.134389	−0.0671943	+	0.997740i	$0.521405\pi$
$20$	−3.82843	−0.856062
$21$	0	0
$22$	−8.24264	−1.75734
$23$	1.41421	0.294884	0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421	0.294884	0.147442	+	0.989071i	$0.452896\pi$
$24$	−6.24264	−1.27427
$25$	1.00000	0.200000
$26$	−2.41421	−0.473466
$27$	−5.65685	−1.08866
$28$	0	0
$29$	−5.65685	−1.05045	−0.525226	−	0.850963i	$-0.676019\pi$
$29$	−5.65685	−1.05045	−0.525226	+	0.850963i	$0.676019\pi$
$30$	3.41421	0.623347
$31$	−1.75736	−0.315631	−0.157816	−	0.987469i	$-0.550445\pi$
$31$	−1.75736	−0.315631	−0.157816	+	0.987469i	$0.550445\pi$
$32$	1.58579	0.280330
$33$	4.82843	0.840521
$34$	2.00000	0.342997
$35$	0	0
$36$	−3.82843	−0.638071
$37$	−8.48528	−1.39497	−0.697486	−	0.716599i	$-0.745698\pi$
$37$	−8.48528	−1.39497	−0.697486	+	0.716599i	$0.745698\pi$
$38$	1.41421	0.229416
$39$	1.41421	0.226455
$40$	4.41421	0.697948
$41$	3.17157	0.495316	0.247658	−	0.968847i	$-0.420339\pi$
$41$	3.17157	0.495316	0.247658	+	0.968847i	$0.420339\pi$
$42$	0	0
$43$	−11.0711	−1.68832	−0.844161	−	0.536090i	$-0.819901\pi$
$43$	−11.0711	−1.68832	−0.844161	+	0.536090i	$0.819901\pi$
$44$	13.0711	1.97054
$45$	1.00000	0.149071
$46$	−3.41421	−0.503398
$47$	4.82843	0.704298	0.352149	−	0.935944i	$-0.385451\pi$
$47$	4.82843	0.704298	0.352149	+	0.935944i	$0.385451\pi$
$48$	4.24264	0.612372
$49$	0	0
$50$	−2.41421	−0.341421
$51$	−1.17157	−0.164053
$52$	3.82843	0.530907
$53$	2.48528	0.341380	0.170690	−	0.985325i	$-0.445400\pi$
$53$	2.48528	0.341380	0.170690	+	0.985325i	$0.445400\pi$
$54$	13.6569	1.85846
$55$	−3.41421	−0.460372
$56$	0	0
$57$	−0.828427	−0.109728
$58$	13.6569	1.79323
$59$	−1.75736	−0.228789	−0.114394	−	0.993435i	$-0.536493\pi$
$59$	−1.75736	−0.228789	−0.114394	+	0.993435i	$0.536493\pi$
$60$	−5.41421	−0.698972
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	4.24264	0.538816
$63$	0	0
$64$	−9.82843	−1.22855
$65$	−1.00000	−0.124035
$66$	−11.6569	−1.43486
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−3.17157	−0.384610
$69$	2.00000	0.240772
$70$	0	0
$71$	11.8995	1.41221	0.706105	−	0.708107i	$-0.250451\pi$
$71$	11.8995	1.41221	0.706105	+	0.708107i	$0.250451\pi$
$72$	4.41421	0.520220
$73$	−8.48528	−0.993127	−0.496564	−	0.868000i	$-0.665405\pi$
$73$	−8.48528	−0.993127	−0.496564	+	0.868000i	$0.665405\pi$
$74$	20.4853	2.38137
$75$	1.41421	0.163299
$76$	−2.24264	−0.257249
$77$	0	0
$78$	−3.41421	−0.386584
$79$	−8.48528	−0.954669	−0.477334	−	0.878722i	$-0.658397\pi$
$79$	−8.48528	−0.954669	−0.477334	+	0.878722i	$0.658397\pi$
$80$	−3.00000	−0.335410
$81$	−5.00000	−0.555556
$82$	−7.65685	−0.845558
$83$	3.17157	0.348125	0.174063	−	0.984735i	$-0.444310\pi$
$83$	3.17157	0.348125	0.174063	+	0.984735i	$0.444310\pi$
$84$	0	0
$85$	0.828427	0.0898555
$86$	26.7279	2.88215
$87$	−8.00000	−0.857690
$88$	−15.0711	−1.60658
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−2.41421	−0.254480
$91$	0	0
$92$	5.41421	0.564471
$93$	−2.48528	−0.257712
$94$	−11.6569	−1.20231
$95$	0.585786	0.0601004
$96$	2.24264	0.228889
$97$	7.65685	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$97$	7.65685	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$98$	0	0
$99$	−3.41421	−0.343141
$100$	3.82843	0.382843
$101$	3.65685	0.363871	0.181935	−	0.983311i	$-0.441764\pi$
$101$	3.65685	0.363871	0.181935	+	0.983311i	$0.441764\pi$
$102$	2.82843	0.280056
$103$	−14.5858	−1.43718	−0.718590	−	0.695434i	$-0.755212\pi$
$103$	−14.5858	−1.43718	−0.718590	+	0.695434i	$0.755212\pi$
$104$	−4.41421	−0.432849
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−9.41421	−0.910106	−0.455053	−	0.890464i	$-0.650380\pi$
$107$	−9.41421	−0.910106	−0.455053	+	0.890464i	$0.650380\pi$
$108$	−21.6569	−2.08393
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	8.24264	0.785905
$111$	−12.0000	−1.13899
$112$	0	0
$113$	−8.82843	−0.830509	−0.415254	−	0.909705i	$-0.636307\pi$
$113$	−8.82843	−0.830509	−0.415254	+	0.909705i	$0.636307\pi$
$114$	2.00000	0.187317
$115$	−1.41421	−0.131876
$116$	−21.6569	−2.01079
$117$	−1.00000	−0.0924500
$118$	4.24264	0.390567
$119$	0	0
$120$	6.24264	0.569873
$121$	0.656854	0.0597140
$122$	−19.3137	−1.74858
$123$	4.48528	0.404424
$124$	−6.72792	−0.604185
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−6.58579	−0.584394	−0.292197	−	0.956358i	$-0.594386\pi$
$127$	−6.58579	−0.584394	−0.292197	+	0.956358i	$0.594386\pi$
$128$	20.5563	1.81694
$129$	−15.6569	−1.37851
$130$	2.41421	0.211741
$131$	16.9706	1.48272	0.741362	−	0.671105i	$-0.234180\pi$
$131$	16.9706	1.48272	0.741362	+	0.671105i	$0.234180\pi$
$132$	18.4853	1.60894
$133$	0	0
$134$	4.82843	0.417113
$135$	5.65685	0.486864
$136$	3.65685	0.313573
$137$	−17.3137	−1.47921	−0.739605	−	0.673041i	$-0.764988\pi$
$137$	−17.3137	−1.47921	−0.739605	+	0.673041i	$0.764988\pi$
$138$	−4.82843	−0.411023
$139$	−4.48528	−0.380437	−0.190218	−	0.981742i	$-0.560920\pi$
$139$	−4.48528	−0.380437	−0.190218	+	0.981742i	$0.560920\pi$
$140$	0	0
$141$	6.82843	0.575057
$142$	−28.7279	−2.41079
$143$	3.41421	0.285511
$144$	−3.00000	−0.250000
$145$	5.65685	0.469776
$146$	20.4853	1.69537
$147$	0	0
$148$	−32.4853	−2.67027
$149$	−11.6569	−0.954967	−0.477483	−	0.878641i	$-0.658451\pi$
$149$	−11.6569	−0.954967	−0.477483	+	0.878641i	$0.658451\pi$
$150$	−3.41421	−0.278769
$151$	9.75736	0.794043	0.397021	−	0.917809i	$-0.370044\pi$
$151$	9.75736	0.794043	0.397021	+	0.917809i	$0.370044\pi$
$152$	2.58579	0.209735
$153$	0.828427	0.0669744
$154$	0	0
$155$	1.75736	0.141154
$156$	5.41421	0.433484
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	20.4853	1.62972
$159$	3.51472	0.278735
$160$	−1.58579	−0.125367
$161$	0	0
$162$	12.0711	0.948393
$163$	18.9706	1.48589	0.742945	−	0.669353i	$-0.233429\pi$
$163$	18.9706	1.48589	0.742945	+	0.669353i	$0.233429\pi$
$164$	12.1421	0.948141
$165$	−4.82843	−0.375893
$166$	−7.65685	−0.594287
$167$	3.17157	0.245424	0.122712	−	0.992442i	$-0.460841\pi$
$167$	3.17157	0.245424	0.122712	+	0.992442i	$0.460841\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−2.00000	−0.153393
$171$	0.585786	0.0447962
$172$	−42.3848	−3.23181
$173$	−16.8284	−1.27944	−0.639721	−	0.768607i	$-0.720950\pi$
$173$	−16.8284	−1.27944	−0.639721	+	0.768607i	$0.720950\pi$
$174$	19.3137	1.46417
$175$	0	0
$176$	10.2426	0.772068
$177$	−2.48528	−0.186805
$178$	14.4853	1.08572
$179$	5.65685	0.422813	0.211407	−	0.977398i	$-0.432196\pi$
$179$	5.65685	0.422813	0.211407	+	0.977398i	$0.432196\pi$
$180$	3.82843	0.285354
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	11.3137	0.836333
$184$	−6.24264	−0.460214
$185$	8.48528	0.623850
$186$	6.00000	0.439941
$187$	−2.82843	−0.206835
$188$	18.4853	1.34818
$189$	0	0
$190$	−1.41421	−0.102598
$191$	2.34315	0.169544	0.0847720	−	0.996400i	$-0.472984\pi$
$191$	2.34315	0.169544	0.0847720	+	0.996400i	$0.472984\pi$
$192$	−13.8995	−1.00311
$193$	4.34315	0.312626	0.156313	−	0.987708i	$-0.450039\pi$
$193$	4.34315	0.312626	0.156313	+	0.987708i	$0.450039\pi$
$194$	−18.4853	−1.32717
$195$	−1.41421	−0.101274
$196$	0	0
$197$	10.9706	0.781620	0.390810	−	0.920471i	$-0.372195\pi$
$197$	10.9706	0.781620	0.390810	+	0.920471i	$0.372195\pi$
$198$	8.24264	0.585779
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−4.41421	−0.312132
$201$	−2.82843	−0.199502
$202$	−8.82843	−0.621166
$203$	0	0
$204$	−4.48528	−0.314033
$205$	−3.17157	−0.221512
$206$	35.2132	2.45342
$207$	−1.41421	−0.0982946
$208$	3.00000	0.208013
$209$	−2.00000	−0.138343
$210$	0	0
$211$	3.31371	0.228125	0.114063	−	0.993474i	$-0.463614\pi$
$211$	3.31371	0.228125	0.114063	+	0.993474i	$0.463614\pi$
$212$	9.51472	0.653474
$213$	16.8284	1.15306
$214$	22.7279	1.55365
$215$	11.0711	0.755041
$216$	24.9706	1.69903
$217$	0	0
$218$	4.82843	0.327022
$219$	−12.0000	−0.810885
$220$	−13.0711	−0.881251
$221$	−0.828427	−0.0557260
$222$	28.9706	1.94438
$223$	−9.51472	−0.637153	−0.318576	−	0.947897i	$-0.603205\pi$
$223$	−9.51472	−0.637153	−0.318576	+	0.947897i	$0.603205\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	21.3137	1.41777
$227$	16.3431	1.08473	0.542366	−	0.840142i	$-0.317528\pi$
$227$	16.3431	1.08473	0.542366	+	0.840142i	$0.317528\pi$
$228$	−3.17157	−0.210043
$229$	4.82843	0.319071	0.159536	−	0.987192i	$-0.449000\pi$
$229$	4.82843	0.319071	0.159536	+	0.987192i	$0.449000\pi$
$230$	3.41421	0.225127
$231$	0	0
$232$	24.9706	1.63940
$233$	−20.6274	−1.35135	−0.675674	−	0.737201i	$-0.736147\pi$
$233$	−20.6274	−1.35135	−0.675674	+	0.737201i	$0.736147\pi$
$234$	2.41421	0.157822
$235$	−4.82843	−0.314972
$236$	−6.72792	−0.437950
$237$	−12.0000	−0.779484
$238$	0	0
$239$	−3.41421	−0.220847	−0.110424	−	0.993885i	$-0.535221\pi$
$239$	−3.41421	−0.220847	−0.110424	+	0.993885i	$0.535221\pi$
$240$	−4.24264	−0.273861
$241$	14.4853	0.933079	0.466539	−	0.884500i	$-0.345501\pi$
$241$	14.4853	0.933079	0.466539	+	0.884500i	$0.345501\pi$
$242$	−1.58579	−0.101938
$243$	9.89949	0.635053
$244$	30.6274	1.96072
$245$	0	0
$246$	−10.8284	−0.690395
$247$	−0.585786	−0.0372727
$248$	7.75736	0.492593
$249$	4.48528	0.284243
$250$	2.41421	0.152688
$251$	−19.7990	−1.24970	−0.624851	−	0.780744i	$-0.714840\pi$
$251$	−19.7990	−1.24970	−0.624851	+	0.780744i	$0.714840\pi$
$252$	0	0
$253$	4.82843	0.303561
$254$	15.8995	0.997623
$255$	1.17157	0.0733667
$256$	−29.9706	−1.87316
$257$	−27.6569	−1.72519	−0.862594	−	0.505898i	$-0.831161\pi$
$257$	−27.6569	−1.72519	−0.862594	+	0.505898i	$0.831161\pi$
$258$	37.7990	2.35326
$259$	0	0
$260$	−3.82843	−0.237429
$261$	5.65685	0.350150
$262$	−40.9706	−2.53117
$263$	−10.5858	−0.652748	−0.326374	−	0.945241i	$-0.605827\pi$
$263$	−10.5858	−0.652748	−0.326374	+	0.945241i	$0.605827\pi$
$264$	−21.3137	−1.31177
$265$	−2.48528	−0.152670
$266$	0	0
$267$	−8.48528	−0.519291
$268$	−7.65685	−0.467717
$269$	25.3137	1.54340	0.771702	−	0.635984i	$-0.219406\pi$
$269$	25.3137	1.54340	0.771702	+	0.635984i	$0.219406\pi$
$270$	−13.6569	−0.831130
$271$	−26.7279	−1.62361	−0.811803	−	0.583932i	$-0.801514\pi$
$271$	−26.7279	−1.62361	−0.811803	+	0.583932i	$0.801514\pi$
$272$	−2.48528	−0.150692
$273$	0	0
$274$	41.7990	2.52517
$275$	3.41421	0.205885
$276$	7.65685	0.460888
$277$	−12.8284	−0.770785	−0.385393	−	0.922753i	$-0.625934\pi$
$277$	−12.8284	−0.770785	−0.385393	+	0.922753i	$0.625934\pi$
$278$	10.8284	0.649446
$279$	1.75736	0.105210
$280$	0	0
$281$	21.7990	1.30042	0.650209	−	0.759755i	$-0.274681\pi$
$281$	21.7990	1.30042	0.650209	+	0.759755i	$0.274681\pi$
$282$	−16.4853	−0.981684
$283$	16.7279	0.994372	0.497186	−	0.867644i	$-0.334367\pi$
$283$	16.7279	0.994372	0.497186	+	0.867644i	$0.334367\pi$
$284$	45.5563	2.70327
$285$	0.828427	0.0490718
$286$	−8.24264	−0.487398
$287$	0	0
$288$	−1.58579	−0.0934434
$289$	−16.3137	−0.959630
$290$	−13.6569	−0.801958
$291$	10.8284	0.634774
$292$	−32.4853	−1.90106
$293$	−26.1421	−1.52724	−0.763620	−	0.645666i	$-0.776580\pi$
$293$	−26.1421	−1.52724	−0.763620	+	0.645666i	$0.776580\pi$
$294$	0	0
$295$	1.75736	0.102317
$296$	37.4558	2.17708
$297$	−19.3137	−1.12070
$298$	28.1421	1.63023
$299$	1.41421	0.0817861
$300$	5.41421	0.312590
$301$	0	0
$302$	−23.5563	−1.35552
$303$	5.17157	0.297099
$304$	−1.75736	−0.100791
$305$	−8.00000	−0.458079
$306$	−2.00000	−0.114332
$307$	−24.8284	−1.41703	−0.708517	−	0.705694i	$-0.750635\pi$
$307$	−24.8284	−1.41703	−0.708517	+	0.705694i	$0.750635\pi$
$308$	0	0
$309$	−20.6274	−1.17345
$310$	−4.24264	−0.240966
$311$	−8.48528	−0.481156	−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528	−0.481156	−0.240578	+	0.970630i	$0.577337\pi$
$312$	−6.24264	−0.353420
$313$	4.82843	0.272919	0.136459	−	0.990646i	$-0.456428\pi$
$313$	4.82843	0.272919	0.136459	+	0.990646i	$0.456428\pi$
$314$	43.4558	2.45236
$315$	0	0
$316$	−32.4853	−1.82744
$317$	−2.14214	−0.120314	−0.0601572	−	0.998189i	$-0.519160\pi$
$317$	−2.14214	−0.120314	−0.0601572	+	0.998189i	$0.519160\pi$
$318$	−8.48528	−0.475831
$319$	−19.3137	−1.08136
$320$	9.82843	0.549426
$321$	−13.3137	−0.743099
$322$	0	0
$323$	0.485281	0.0270018
$324$	−19.1421	−1.06345
$325$	1.00000	0.0554700
$326$	−45.7990	−2.53657
$327$	−2.82843	−0.156412
$328$	−14.0000	−0.773021
$329$	0	0
$330$	11.6569	0.641689
$331$	−26.0416	−1.43138	−0.715689	−	0.698419i	$-0.753887\pi$
$331$	−26.0416	−1.43138	−0.715689	+	0.698419i	$0.753887\pi$
$332$	12.1421	0.666386
$333$	8.48528	0.464991
$334$	−7.65685	−0.418964
$335$	2.00000	0.109272
$336$	0	0
$337$	12.8284	0.698809	0.349404	−	0.936972i	$-0.386384\pi$
$337$	12.8284	0.698809	0.349404	+	0.936972i	$0.386384\pi$
$338$	−2.41421	−0.131316
$339$	−12.4853	−0.678107
$340$	3.17157	0.172003
$341$	−6.00000	−0.324918
$342$	−1.41421	−0.0764719
$343$	0	0
$344$	48.8701	2.63490
$345$	−2.00000	−0.107676
$346$	40.6274	2.18414
$347$	−4.24264	−0.227757	−0.113878	−	0.993495i	$-0.536327\pi$
$347$	−4.24264	−0.227757	−0.113878	+	0.993495i	$0.536327\pi$
$348$	−30.6274	−1.64180
$349$	−18.4853	−0.989494	−0.494747	−	0.869037i	$-0.664739\pi$
$349$	−18.4853	−0.989494	−0.494747	+	0.869037i	$0.664739\pi$
$350$	0	0
$351$	−5.65685	−0.301941
$352$	5.41421	0.288579
$353$	−14.8284	−0.789238	−0.394619	−	0.918845i	$-0.629123\pi$
$353$	−14.8284	−0.789238	−0.394619	+	0.918845i	$0.629123\pi$
$354$	6.00000	0.318896
$355$	−11.8995	−0.631560
$356$	−22.9706	−1.21744
$357$	0	0
$358$	−13.6569	−0.721787
$359$	−8.10051	−0.427528	−0.213764	−	0.976885i	$-0.568572\pi$
$359$	−8.10051	−0.427528	−0.213764	+	0.976885i	$0.568572\pi$
$360$	−4.41421	−0.232649
$361$	−18.6569	−0.981940
$362$	0	0
$363$	0.928932	0.0487563
$364$	0	0
$365$	8.48528	0.444140
$366$	−27.3137	−1.42771
$367$	−35.5563	−1.85603	−0.928013	−	0.372547i	$-0.878484\pi$
$367$	−35.5563	−1.85603	−0.928013	+	0.372547i	$0.878484\pi$
$368$	4.24264	0.221163
$369$	−3.17157	−0.165105
$370$	−20.4853	−1.06498
$371$	0	0
$372$	−9.51472	−0.493315
$373$	−2.68629	−0.139091	−0.0695455	−	0.997579i	$-0.522155\pi$
$373$	−2.68629	−0.139091	−0.0695455	+	0.997579i	$0.522155\pi$
$374$	6.82843	0.353090
$375$	−1.41421	−0.0730297
$376$	−21.3137	−1.09917
$377$	−5.65685	−0.291343
$378$	0	0
$379$	29.0711	1.49328	0.746640	−	0.665228i	$-0.231666\pi$
$379$	29.0711	1.49328	0.746640	+	0.665228i	$0.231666\pi$
$380$	2.24264	0.115045
$381$	−9.31371	−0.477156
$382$	−5.65685	−0.289430
$383$	29.1127	1.48759	0.743795	−	0.668408i	$-0.233024\pi$
$383$	29.1127	1.48759	0.743795	+	0.668408i	$0.233024\pi$
$384$	29.0711	1.48353
$385$	0	0
$386$	−10.4853	−0.533687
$387$	11.0711	0.562774
$388$	29.3137	1.48818
$389$	28.6274	1.45147	0.725734	−	0.687976i	$-0.241500\pi$
$389$	28.6274	1.45147	0.725734	+	0.687976i	$0.241500\pi$
$390$	3.41421	0.172885
$391$	−1.17157	−0.0592490
$392$	0	0
$393$	24.0000	1.21064
$394$	−26.4853	−1.33431
$395$	8.48528	0.426941
$396$	−13.0711	−0.656846
$397$	−11.7990	−0.592174	−0.296087	−	0.955161i	$-0.595682\pi$
$397$	−11.7990	−0.592174	−0.296087	+	0.955161i	$0.595682\pi$
$398$	9.65685	0.484054
$399$	0	0
$400$	3.00000	0.150000
$401$	−5.31371	−0.265354	−0.132677	−	0.991159i	$-0.542357\pi$
$401$	−5.31371	−0.265354	−0.132677	+	0.991159i	$0.542357\pi$
$402$	6.82843	0.340571
$403$	−1.75736	−0.0875403
$404$	14.0000	0.696526
$405$	5.00000	0.248452
$406$	0	0
$407$	−28.9706	−1.43602
$408$	5.17157	0.256031
$409$	−7.17157	−0.354611	−0.177306	−	0.984156i	$-0.556738\pi$
$409$	−7.17157	−0.354611	−0.177306	+	0.984156i	$0.556738\pi$
$410$	7.65685	0.378145
$411$	−24.4853	−1.20777
$412$	−55.8406	−2.75107
$413$	0	0
$414$	3.41421	0.167799
$415$	−3.17157	−0.155686
$416$	1.58579	0.0777496
$417$	−6.34315	−0.310625
$418$	4.82843	0.236166
$419$	−10.8284	−0.529003	−0.264502	−	0.964385i	$-0.585207\pi$
$419$	−10.8284	−0.529003	−0.264502	+	0.964385i	$0.585207\pi$
$420$	0	0
$421$	−34.9706	−1.70436	−0.852180	−	0.523248i	$-0.824720\pi$
$421$	−34.9706	−1.70436	−0.852180	+	0.523248i	$0.824720\pi$
$422$	−8.00000	−0.389434
$423$	−4.82843	−0.234766
$424$	−10.9706	−0.532778
$425$	−0.828427	−0.0401846
$426$	−40.6274	−1.96840
$427$	0	0
$428$	−36.0416	−1.74214
$429$	4.82843	0.233119
$430$	−26.7279	−1.28893
$431$	40.3848	1.94527	0.972633	−	0.232346i	$-0.0746403\pi$
$431$	40.3848	1.94527	0.972633	+	0.232346i	$0.0746403\pi$
$432$	−16.9706	−0.816497
$433$	−7.65685	−0.367965	−0.183982	−	0.982930i	$-0.558899\pi$
$433$	−7.65685	−0.367965	−0.183982	+	0.982930i	$0.558899\pi$
$434$	0	0
$435$	8.00000	0.383571
$436$	−7.65685	−0.366697
$437$	−0.828427	−0.0396290
$438$	28.9706	1.38427
$439$	−0.970563	−0.0463224	−0.0231612	−	0.999732i	$-0.507373\pi$
$439$	−0.970563	−0.0463224	−0.0231612	+	0.999732i	$0.507373\pi$
$440$	15.0711	0.718485
$441$	0	0
$442$	2.00000	0.0951303
$443$	−9.41421	−0.447283	−0.223641	−	0.974671i	$-0.571794\pi$
$443$	−9.41421	−0.447283	−0.223641	+	0.974671i	$0.571794\pi$
$444$	−45.9411	−2.18027
$445$	6.00000	0.284427
$446$	22.9706	1.08769
$447$	−16.4853	−0.779727
$448$	0	0
$449$	−33.1127	−1.56268	−0.781342	−	0.624103i	$-0.785465\pi$
$449$	−33.1127	−1.56268	−0.781342	+	0.624103i	$0.785465\pi$
$450$	2.41421	0.113807
$451$	10.8284	0.509891
$452$	−33.7990	−1.58977
$453$	13.7990	0.648333
$454$	−39.4558	−1.85175
$455$	0	0
$456$	3.65685	0.171248
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−11.6569	−0.544689
$459$	4.68629	0.218737
$460$	−5.41421	−0.252439
$461$	−9.51472	−0.443145	−0.221572	−	0.975144i	$-0.571119\pi$
$461$	−9.51472	−0.443145	−0.221572	+	0.975144i	$0.571119\pi$
$462$	0	0
$463$	−4.34315	−0.201843	−0.100922	−	0.994894i	$-0.532179\pi$
$463$	−4.34315	−0.201843	−0.100922	+	0.994894i	$0.532179\pi$
$464$	−16.9706	−0.787839
$465$	2.48528	0.115252
$466$	49.7990	2.30689
$467$	13.4142	0.620736	0.310368	−	0.950617i	$-0.399548\pi$
$467$	13.4142	0.620736	0.310368	+	0.950617i	$0.399548\pi$
$468$	−3.82843	−0.176969
$469$	0	0
$470$	11.6569	0.537691
$471$	−25.4558	−1.17294
$472$	7.75736	0.357061
$473$	−37.7990	−1.73800
$474$	28.9706	1.33066
$475$	−0.585786	−0.0268777
$476$	0	0
$477$	−2.48528	−0.113793
$478$	8.24264	0.377010
$479$	30.7279	1.40399	0.701997	−	0.712180i	$-0.252292\pi$
$479$	30.7279	1.40399	0.701997	+	0.712180i	$0.252292\pi$
$480$	−2.24264	−0.102362
$481$	−8.48528	−0.386896
$482$	−34.9706	−1.59287
$483$	0	0
$484$	2.51472	0.114305
$485$	−7.65685	−0.347680
$486$	−23.8995	−1.08410
$487$	−10.9706	−0.497124	−0.248562	−	0.968616i	$-0.579958\pi$
$487$	−10.9706	−0.497124	−0.248562	+	0.968616i	$0.579958\pi$
$488$	−35.3137	−1.59858
$489$	26.8284	1.21322
$490$	0	0
$491$	5.17157	0.233390	0.116695	−	0.993168i	$-0.462770\pi$
$491$	5.17157	0.233390	0.116695	+	0.993168i	$0.462770\pi$
$492$	17.1716	0.774154
$493$	4.68629	0.211060
$494$	1.41421	0.0636285
$495$	3.41421	0.153457
$496$	−5.27208	−0.236723
$497$	0	0
$498$	−10.8284	−0.485233
$499$	41.5563	1.86032	0.930159	−	0.367157i	$-0.119669\pi$
$499$	41.5563	1.86032	0.930159	+	0.367157i	$0.119669\pi$
$500$	−3.82843	−0.171212
$501$	4.48528	0.200388
$502$	47.7990	2.13337
$503$	−37.8995	−1.68985	−0.844927	−	0.534881i	$-0.820356\pi$
$503$	−37.8995	−1.68985	−0.844927	+	0.534881i	$0.820356\pi$
$504$	0	0
$505$	−3.65685	−0.162728
$506$	−11.6569	−0.518210
$507$	1.41421	0.0628074
$508$	−25.2132	−1.11866
$509$	−41.1127	−1.82229	−0.911144	−	0.412088i	$-0.864800\pi$
$509$	−41.1127	−1.82229	−0.911144	+	0.412088i	$0.864800\pi$
$510$	−2.82843	−0.125245
$511$	0	0
$512$	31.2426	1.38074
$513$	3.31371	0.146304
$514$	66.7696	2.94508
$515$	14.5858	0.642727
$516$	−59.9411	−2.63876
$517$	16.4853	0.725022
$518$	0	0
$519$	−23.7990	−1.04466
$520$	4.41421	0.193576
$521$	17.6569	0.773561	0.386780	−	0.922172i	$-0.373587\pi$
$521$	17.6569	0.773561	0.386780	+	0.922172i	$0.373587\pi$
$522$	−13.6569	−0.597744
$523$	19.7574	0.863929	0.431965	−	0.901891i	$-0.357821\pi$
$523$	19.7574	0.863929	0.431965	+	0.901891i	$0.357821\pi$
$524$	64.9706	2.83825
$525$	0	0
$526$	25.5563	1.11431
$527$	1.45584	0.0634176
$528$	14.4853	0.630391
$529$	−21.0000	−0.913043
$530$	6.00000	0.260623
$531$	1.75736	0.0762629
$532$	0	0
$533$	3.17157	0.137376
$534$	20.4853	0.886485
$535$	9.41421	0.407012
$536$	8.82843	0.381330
$537$	8.00000	0.345225
$538$	−61.1127	−2.63476
$539$	0	0
$540$	21.6569	0.931963
$541$	−7.17157	−0.308330	−0.154165	−	0.988045i	$-0.549269\pi$
$541$	−7.17157	−0.308330	−0.154165	+	0.988045i	$0.549269\pi$
$542$	64.5269	2.77167
$543$	0	0
$544$	−1.31371	−0.0563248
$545$	2.00000	0.0856706
$546$	0	0
$547$	13.2132	0.564956	0.282478	−	0.959274i	$-0.408844\pi$
$547$	13.2132	0.564956	0.282478	+	0.959274i	$0.408844\pi$
$548$	−66.2843	−2.83152
$549$	−8.00000	−0.341432
$550$	−8.24264	−0.351467
$551$	3.31371	0.141169
$552$	−8.82843	−0.375763
$553$	0	0
$554$	30.9706	1.31581
$555$	12.0000	0.509372
$556$	−17.1716	−0.728237
$557$	−35.7990	−1.51685	−0.758426	−	0.651759i	$-0.774031\pi$
$557$	−35.7990	−1.51685	−0.758426	+	0.651759i	$0.774031\pi$
$558$	−4.24264	−0.179605
$559$	−11.0711	−0.468256
$560$	0	0
$561$	−4.00000	−0.168880
$562$	−52.6274	−2.21995
$563$	7.75736	0.326934	0.163467	−	0.986549i	$-0.447732\pi$
$563$	7.75736	0.326934	0.163467	+	0.986549i	$0.447732\pi$
$564$	26.1421	1.10078
$565$	8.82843	0.371415
$566$	−40.3848	−1.69750
$567$	0	0
$568$	−52.5269	−2.20398
$569$	−10.3431	−0.433607	−0.216804	−	0.976215i	$-0.569563\pi$
$569$	−10.3431	−0.433607	−0.216804	+	0.976215i	$0.569563\pi$
$570$	−2.00000	−0.0837708
$571$	−11.5147	−0.481876	−0.240938	−	0.970541i	$-0.577455\pi$
$571$	−11.5147	−0.481876	−0.240938	+	0.970541i	$0.577455\pi$
$572$	13.0711	0.546529
$573$	3.31371	0.138432
$574$	0	0
$575$	1.41421	0.0589768
$576$	9.82843	0.409518
$577$	34.8284	1.44993	0.724963	−	0.688788i	$-0.241857\pi$
$577$	34.8284	1.44993	0.724963	+	0.688788i	$0.241857\pi$
$578$	39.3848	1.63819
$579$	6.14214	0.255258
$580$	21.6569	0.899252
$581$	0	0
$582$	−26.1421	−1.08363
$583$	8.48528	0.351424
$584$	37.4558	1.54993
$585$	1.00000	0.0413449
$586$	63.1127	2.60716
$587$	−20.3431	−0.839651	−0.419826	−	0.907605i	$-0.637909\pi$
$587$	−20.3431	−0.839651	−0.419826	+	0.907605i	$0.637909\pi$
$588$	0	0
$589$	1.02944	0.0424172
$590$	−4.24264	−0.174667
$591$	15.5147	0.638190
$592$	−25.4558	−1.04623
$593$	24.6274	1.01133	0.505663	−	0.862731i	$-0.331248\pi$
$593$	24.6274	1.01133	0.505663	+	0.862731i	$0.331248\pi$
$594$	46.6274	1.91315
$595$	0	0
$596$	−44.6274	−1.82801
$597$	−5.65685	−0.231520
$598$	−3.41421	−0.139618
$599$	25.4558	1.04010	0.520049	−	0.854137i	$-0.325914\pi$
$599$	25.4558	1.04010	0.520049	+	0.854137i	$0.325914\pi$
$600$	−6.24264	−0.254855
$601$	44.6274	1.82039	0.910195	−	0.414180i	$-0.135931\pi$
$601$	44.6274	1.82039	0.910195	+	0.414180i	$0.135931\pi$
$602$	0	0
$603$	2.00000	0.0814463
$604$	37.3553	1.51997
$605$	−0.656854	−0.0267049
$606$	−12.4853	−0.507180
$607$	−31.7574	−1.28899	−0.644496	−	0.764608i	$-0.722933\pi$
$607$	−31.7574	−1.28899	−0.644496	+	0.764608i	$0.722933\pi$
$608$	−0.928932	−0.0376732
$609$	0	0
$610$	19.3137	0.781989
$611$	4.82843	0.195337
$612$	3.17157	0.128203
$613$	−14.6863	−0.593174	−0.296587	−	0.955006i	$-0.595848\pi$
$613$	−14.6863	−0.593174	−0.296587	+	0.955006i	$0.595848\pi$
$614$	59.9411	2.41903
$615$	−4.48528	−0.180864
$616$	0	0
$617$	10.9706	0.441658	0.220829	−	0.975313i	$-0.429124\pi$
$617$	10.9706	0.441658	0.220829	+	0.975313i	$0.429124\pi$
$618$	49.7990	2.00321
$619$	−1.75736	−0.0706342	−0.0353171	−	0.999376i	$-0.511244\pi$
$619$	−1.75736	−0.0706342	−0.0353171	+	0.999376i	$0.511244\pi$
$620$	6.72792	0.270200
$621$	−8.00000	−0.321029
$622$	20.4853	0.821385
$623$	0	0
$624$	4.24264	0.169842
$625$	1.00000	0.0400000
$626$	−11.6569	−0.465902
$627$	−2.82843	−0.112956
$628$	−68.9117	−2.74988
$629$	7.02944	0.280282
$630$	0	0
$631$	−9.75736	−0.388434	−0.194217	−	0.980959i	$-0.562217\pi$
$631$	−9.75736	−0.388434	−0.194217	+	0.980959i	$0.562217\pi$
$632$	37.4558	1.48991
$633$	4.68629	0.186263
$634$	5.17157	0.205389
$635$	6.58579	0.261349
$636$	13.4558	0.533559
$637$	0	0
$638$	46.6274	1.84600
$639$	−11.8995	−0.470737
$640$	−20.5563	−0.812561
$641$	47.6569	1.88233	0.941166	−	0.337944i	$-0.109731\pi$
$641$	47.6569	1.88233	0.941166	+	0.337944i	$0.109731\pi$
$642$	32.1421	1.26855
$643$	−9.51472	−0.375224	−0.187612	−	0.982243i	$-0.560075\pi$
$643$	−9.51472	−0.375224	−0.187612	+	0.982243i	$0.560075\pi$
$644$	0	0
$645$	15.6569	0.616488
$646$	−1.17157	−0.0460949
$647$	−9.41421	−0.370111	−0.185055	−	0.982728i	$-0.559246\pi$
$647$	−9.41421	−0.370111	−0.185055	+	0.982728i	$0.559246\pi$
$648$	22.0711	0.867033
$649$	−6.00000	−0.235521
$650$	−2.41421	−0.0946932
$651$	0	0
$652$	72.6274	2.84431
$653$	46.9706	1.83810	0.919050	−	0.394141i	$-0.128958\pi$
$653$	46.9706	1.83810	0.919050	+	0.394141i	$0.128958\pi$
$654$	6.82843	0.267013
$655$	−16.9706	−0.663095
$656$	9.51472	0.371487
$657$	8.48528	0.331042
$658$	0	0
$659$	17.8579	0.695644	0.347822	−	0.937561i	$-0.386921\pi$
$659$	17.8579	0.695644	0.347822	+	0.937561i	$0.386921\pi$
$660$	−18.4853	−0.719539
$661$	−29.5980	−1.15123	−0.575614	−	0.817722i	$-0.695237\pi$
$661$	−29.5980	−1.15123	−0.575614	+	0.817722i	$0.695237\pi$
$662$	62.8701	2.44351
$663$	−1.17157	−0.0455001
$664$	−14.0000	−0.543305
$665$	0	0
$666$	−20.4853	−0.793789
$667$	−8.00000	−0.309761
$668$	12.1421	0.469793
$669$	−13.4558	−0.520233
$670$	−4.82843	−0.186538
$671$	27.3137	1.05443
$672$	0	0
$673$	6.48528	0.249989	0.124995	−	0.992157i	$-0.460109\pi$
$673$	6.48528	0.249989	0.124995	+	0.992157i	$0.460109\pi$
$674$	−30.9706	−1.19294
$675$	−5.65685	−0.217732
$676$	3.82843	0.147247
$677$	20.1421	0.774125	0.387063	−	0.922053i	$-0.373490\pi$
$677$	20.1421	0.774125	0.387063	+	0.922053i	$0.373490\pi$
$678$	30.1421	1.15760
$679$	0	0
$680$	−3.65685	−0.140234
$681$	23.1127	0.885681
$682$	14.4853	0.554670
$683$	10.6863	0.408900	0.204450	−	0.978877i	$-0.434459\pi$
$683$	10.6863	0.408900	0.204450	+	0.978877i	$0.434459\pi$
$684$	2.24264	0.0857495
$685$	17.3137	0.661523
$686$	0	0
$687$	6.82843	0.260521
$688$	−33.2132	−1.26624
$689$	2.48528	0.0946817
$690$	4.82843	0.183815
$691$	−6.92893	−0.263589	−0.131795	−	0.991277i	$-0.542074\pi$
$691$	−6.92893	−0.263589	−0.131795	+	0.991277i	$0.542074\pi$
$692$	−64.4264	−2.44912
$693$	0	0
$694$	10.2426	0.388805
$695$	4.48528	0.170136
$696$	35.3137	1.33856
$697$	−2.62742	−0.0995205
$698$	44.6274	1.68917
$699$	−29.1716	−1.10337
$700$	0	0
$701$	14.6863	0.554694	0.277347	−	0.960770i	$-0.410545\pi$
$701$	14.6863	0.554694	0.277347	+	0.960770i	$0.410545\pi$
$702$	13.6569	0.515445
$703$	4.97056	0.187468
$704$	−33.5563	−1.26470
$705$	−6.82843	−0.257173
$706$	35.7990	1.34731
$707$	0	0
$708$	−9.51472	−0.357585
$709$	45.1127	1.69424	0.847121	−	0.531399i	$-0.178334\pi$
$709$	45.1127	1.69424	0.847121	+	0.531399i	$0.178334\pi$
$710$	28.7279	1.07814
$711$	8.48528	0.318223
$712$	26.4853	0.992578
$713$	−2.48528	−0.0930745
$714$	0	0
$715$	−3.41421	−0.127684
$716$	21.6569	0.809355
$717$	−4.82843	−0.180321
$718$	19.5563	0.729836
$719$	−28.9706	−1.08042	−0.540210	−	0.841530i	$-0.681655\pi$
$719$	−28.9706	−1.08042	−0.540210	+	0.841530i	$0.681655\pi$
$720$	3.00000	0.111803
$721$	0	0
$722$	45.0416	1.67628
$723$	20.4853	0.761856
$724$	0	0
$725$	−5.65685	−0.210090
$726$	−2.24264	−0.0832322
$727$	51.3553	1.90466	0.952332	−	0.305063i	$-0.0986777\pi$
$727$	51.3553	1.90466	0.952332	+	0.305063i	$0.0986777\pi$
$728$	0	0
$729$	29.0000	1.07407
$730$	−20.4853	−0.758194
$731$	9.17157	0.339223
$732$	43.3137	1.60092
$733$	−21.3137	−0.787240	−0.393620	−	0.919273i	$-0.628777\pi$
$733$	−21.3137	−0.787240	−0.393620	+	0.919273i	$0.628777\pi$
$734$	85.8406	3.16844
$735$	0	0
$736$	2.24264	0.0826648
$737$	−6.82843	−0.251528
$738$	7.65685	0.281853
$739$	5.27208	0.193937	0.0969683	−	0.995287i	$-0.469085\pi$
$739$	5.27208	0.193937	0.0969683	+	0.995287i	$0.469085\pi$
$740$	32.4853	1.19418
$741$	−0.828427	−0.0304330
$742$	0	0
$743$	−21.5147	−0.789298	−0.394649	−	0.918832i	$-0.629134\pi$
$743$	−21.5147	−0.789298	−0.394649	+	0.918832i	$0.629134\pi$
$744$	10.9706	0.402200
$745$	11.6569	0.427074
$746$	6.48528	0.237443
$747$	−3.17157	−0.116042
$748$	−10.8284	−0.395927
$749$	0	0
$750$	3.41421	0.124669
$751$	−27.5147	−1.00403	−0.502013	−	0.864860i	$-0.667407\pi$
$751$	−27.5147	−1.00403	−0.502013	+	0.864860i	$0.667407\pi$
$752$	14.4853	0.528224
$753$	−28.0000	−1.02038
$754$	13.6569	0.497353
$755$	−9.75736	−0.355107
$756$	0	0
$757$	−24.1421	−0.877461	−0.438730	−	0.898619i	$-0.644572\pi$
$757$	−24.1421	−0.877461	−0.438730	+	0.898619i	$0.644572\pi$
$758$	−70.1838	−2.54919
$759$	6.82843	0.247856
$760$	−2.58579	−0.0937963
$761$	−8.62742	−0.312744	−0.156372	−	0.987698i	$-0.549980\pi$
$761$	−8.62742	−0.312744	−0.156372	+	0.987698i	$0.549980\pi$
$762$	22.4853	0.814556
$763$	0	0
$764$	8.97056	0.324544
$765$	−0.828427	−0.0299518
$766$	−70.2843	−2.53947
$767$	−1.75736	−0.0634546
$768$	−42.3848	−1.52943
$769$	22.9706	0.828340	0.414170	−	0.910200i	$-0.364072\pi$
$769$	22.9706	0.828340	0.414170	+	0.910200i	$0.364072\pi$
$770$	0	0
$771$	−39.1127	−1.40861
$772$	16.6274	0.598434
$773$	22.1421	0.796397	0.398199	−	0.917299i	$-0.369635\pi$
$773$	22.1421	0.796397	0.398199	+	0.917299i	$0.369635\pi$
$774$	−26.7279	−0.960715
$775$	−1.75736	−0.0631262
$776$	−33.7990	−1.21331
$777$	0	0
$778$	−69.1127	−2.47781
$779$	−1.85786	−0.0665649
$780$	−5.41421	−0.193860
$781$	40.6274	1.45376
$782$	2.82843	0.101144
$783$	32.0000	1.14359
$784$	0	0
$785$	18.0000	0.642448
$786$	−57.9411	−2.06669
$787$	−22.4853	−0.801514	−0.400757	−	0.916184i	$-0.631253\pi$
$787$	−22.4853	−0.801514	−0.400757	+	0.916184i	$0.631253\pi$
$788$	42.0000	1.49619
$789$	−14.9706	−0.532966
$790$	−20.4853	−0.728834
$791$	0	0
$792$	15.0711	0.535527
$793$	8.00000	0.284088
$794$	28.4853	1.01090
$795$	−3.51472	−0.124654
$796$	−15.3137	−0.542780
$797$	22.9706	0.813659	0.406830	−	0.913504i	$-0.366634\pi$
$797$	22.9706	0.813659	0.406830	+	0.913504i	$0.366634\pi$
$798$	0	0
$799$	−4.00000	−0.141510
$800$	1.58579	0.0560660
$801$	6.00000	0.212000
$802$	12.8284	0.452988
$803$	−28.9706	−1.02235
$804$	−10.8284	−0.381889
$805$	0	0
$806$	4.24264	0.149441
$807$	35.7990	1.26018
$808$	−16.1421	−0.567878
$809$	45.2548	1.59108	0.795538	−	0.605904i	$-0.207189\pi$
$809$	45.2548	1.59108	0.795538	+	0.605904i	$0.207189\pi$
$810$	−12.0711	−0.424134
$811$	28.3848	0.996724	0.498362	−	0.866969i	$-0.333935\pi$
$811$	28.3848	0.996724	0.498362	+	0.866969i	$0.333935\pi$
$812$	0	0
$813$	−37.7990	−1.32567
$814$	69.9411	2.45144
$815$	−18.9706	−0.664510
$816$	−3.51472	−0.123040
$817$	6.48528	0.226891
$818$	17.3137	0.605360
$819$	0	0
$820$	−12.1421	−0.424022
$821$	−51.2548	−1.78881	−0.894403	−	0.447262i	$-0.852399\pi$
$821$	−51.2548	−1.78881	−0.894403	+	0.447262i	$0.852399\pi$
$822$	59.1127	2.06179
$823$	−2.38478	−0.0831281	−0.0415640	−	0.999136i	$-0.513234\pi$
$823$	−2.38478	−0.0831281	−0.0415640	+	0.999136i	$0.513234\pi$
$824$	64.3848	2.24295
$825$	4.82843	0.168104
$826$	0	0
$827$	56.1421	1.95225	0.976127	−	0.217202i	$-0.0696930\pi$
$827$	56.1421	1.95225	0.976127	+	0.217202i	$0.0696930\pi$
$828$	−5.41421	−0.188157
$829$	−40.9706	−1.42297	−0.711483	−	0.702703i	$-0.751976\pi$
$829$	−40.9706	−1.42297	−0.711483	+	0.702703i	$0.751976\pi$
$830$	7.65685	0.265773
$831$	−18.1421	−0.629344
$832$	−9.82843	−0.340739
$833$	0	0
$834$	15.3137	0.530270
$835$	−3.17157	−0.109757
$836$	−7.65685	−0.264818
$837$	9.94113	0.343616
$838$	26.1421	0.903065
$839$	−6.72792	−0.232274	−0.116137	−	0.993233i	$-0.537051\pi$
$839$	−6.72792	−0.232274	−0.116137	+	0.993233i	$0.537051\pi$
$840$	0	0
$841$	3.00000	0.103448
$842$	84.4264	2.90953
$843$	30.8284	1.06179
$844$	12.6863	0.436680
$845$	−1.00000	−0.0344010
$846$	11.6569	0.400771
$847$	0	0
$848$	7.45584	0.256035
$849$	23.6569	0.811901
$850$	2.00000	0.0685994
$851$	−12.0000	−0.411355
$852$	64.4264	2.20721
$853$	13.4558	0.460719	0.230360	−	0.973106i	$-0.426010\pi$
$853$	13.4558	0.460719	0.230360	+	0.973106i	$0.426010\pi$
$854$	0	0
$855$	−0.585786	−0.0200335
$856$	41.5563	1.42037
$857$	−11.6569	−0.398191	−0.199095	−	0.979980i	$-0.563800\pi$
$857$	−11.6569	−0.398191	−0.199095	+	0.979980i	$0.563800\pi$
$858$	−11.6569	−0.397958
$859$	27.7990	0.948489	0.474245	−	0.880393i	$-0.342721\pi$
$859$	27.7990	0.948489	0.474245	+	0.880393i	$0.342721\pi$
$860$	42.3848	1.44531
$861$	0	0
$862$	−97.4975	−3.32078
$863$	−31.4558	−1.07077	−0.535385	−	0.844608i	$-0.679833\pi$
$863$	−31.4558	−1.07077	−0.535385	+	0.844608i	$0.679833\pi$
$864$	−8.97056	−0.305185
$865$	16.8284	0.572184
$866$	18.4853	0.628155
$867$	−23.0711	−0.783535
$868$	0	0
$869$	−28.9706	−0.982759
$870$	−19.3137	−0.654796
$871$	−2.00000	−0.0677674
$872$	8.82843	0.298968
$873$	−7.65685	−0.259145
$874$	2.00000	0.0676510
$875$	0	0
$876$	−45.9411	−1.55221
$877$	25.3137	0.854783	0.427392	−	0.904067i	$-0.359433\pi$
$877$	25.3137	0.854783	0.427392	+	0.904067i	$0.359433\pi$
$878$	2.34315	0.0790773
$879$	−36.9706	−1.24699
$880$	−10.2426	−0.345279
$881$	−19.0294	−0.641118	−0.320559	−	0.947229i	$-0.603871\pi$
$881$	−19.0294	−0.641118	−0.320559	+	0.947229i	$0.603871\pi$
$882$	0	0
$883$	−23.7574	−0.799499	−0.399749	−	0.916624i	$-0.630903\pi$
$883$	−23.7574	−0.799499	−0.399749	+	0.916624i	$0.630903\pi$
$884$	−3.17157	−0.106672
$885$	2.48528	0.0835418
$886$	22.7279	0.763559
$887$	22.3848	0.751607	0.375804	−	0.926699i	$-0.377367\pi$
$887$	22.3848	0.751607	0.375804	+	0.926699i	$0.377367\pi$
$888$	52.9706	1.77758
$889$	0	0
$890$	−14.4853	−0.485548
$891$	−17.0711	−0.571902
$892$	−36.4264	−1.21965
$893$	−2.82843	−0.0946497
$894$	39.7990	1.33108
$895$	−5.65685	−0.189088
$896$	0	0
$897$	2.00000	0.0667781
$898$	79.9411	2.66767
$899$	9.94113	0.331555
$900$	−3.82843	−0.127614
$901$	−2.05887	−0.0685911
$902$	−26.1421	−0.870438
$903$	0	0
$904$	38.9706	1.29614
$905$	0	0
$906$	−33.3137	−1.10677
$907$	9.21320	0.305919	0.152960	−	0.988232i	$-0.451120\pi$
$907$	9.21320	0.305919	0.152960	+	0.988232i	$0.451120\pi$
$908$	62.5685	2.07641
$909$	−3.65685	−0.121290
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−2.48528	−0.0822959
$913$	10.8284	0.358369
$914$	43.4558	1.43739
$915$	−11.3137	−0.374020
$916$	18.4853	0.610771
$917$	0	0
$918$	−11.3137	−0.373408
$919$	0.485281	0.0160080	0.00800398	−	0.999968i	$-0.497452\pi$
$919$	0.485281	0.0160080	0.00800398	+	0.999968i	$0.497452\pi$
$920$	6.24264	0.205814
$921$	−35.1127	−1.15700
$922$	22.9706	0.756495
$923$	11.8995	0.391677
$924$	0	0
$925$	−8.48528	−0.278994
$926$	10.4853	0.344568
$927$	14.5858	0.479060
$928$	−8.97056	−0.294473
$929$	−16.8284	−0.552123	−0.276061	−	0.961140i	$-0.589029\pi$
$929$	−16.8284	−0.552123	−0.276061	+	0.961140i	$0.589029\pi$
$930$	−6.00000	−0.196748
$931$	0	0
$932$	−78.9706	−2.58677
$933$	−12.0000	−0.392862
$934$	−32.3848	−1.05966
$935$	2.82843	0.0924995
$936$	4.41421	0.144283
$937$	22.9706	0.750416	0.375208	−	0.926941i	$-0.377571\pi$
$937$	22.9706	0.750416	0.375208	+	0.926941i	$0.377571\pi$
$938$	0	0
$939$	6.82843	0.222837
$940$	−18.4853	−0.602923
$941$	−18.7696	−0.611870	−0.305935	−	0.952052i	$-0.598969\pi$
$941$	−18.7696	−0.611870	−0.305935	+	0.952052i	$0.598969\pi$
$942$	61.4558	2.00234
$943$	4.48528	0.146061
$944$	−5.27208	−0.171592
$945$	0	0
$946$	91.2548	2.96695
$947$	17.1127	0.556088	0.278044	−	0.960568i	$-0.410314\pi$
$947$	17.1127	0.556088	0.278044	+	0.960568i	$0.410314\pi$
$948$	−45.9411	−1.49210
$949$	−8.48528	−0.275444
$950$	1.41421	0.0458831
$951$	−3.02944	−0.0982362
$952$	0	0
$953$	35.2548	1.14202	0.571008	−	0.820944i	$-0.306553\pi$
$953$	35.2548	1.14202	0.571008	+	0.820944i	$0.306553\pi$
$954$	6.00000	0.194257
$955$	−2.34315	−0.0758224
$956$	−13.0711	−0.422749
$957$	−27.3137	−0.882927
$958$	−74.1838	−2.39677
$959$	0	0
$960$	13.8995	0.448604
$961$	−27.9117	−0.900377
$962$	20.4853	0.660472
$963$	9.41421	0.303369
$964$	55.4558	1.78611
$965$	−4.34315	−0.139811
$966$	0	0
$967$	47.9411	1.54168	0.770841	−	0.637027i	$-0.219836\pi$
$967$	47.9411	1.54168	0.770841	+	0.637027i	$0.219836\pi$
$968$	−2.89949	−0.0931933
$969$	0.686292	0.0220469
$970$	18.4853	0.593527
$971$	−44.2843	−1.42115	−0.710575	−	0.703622i	$-0.751565\pi$
$971$	−44.2843	−1.42115	−0.710575	+	0.703622i	$0.751565\pi$
$972$	37.8995	1.21563
$973$	0	0
$974$	26.4853	0.848643
$975$	1.41421	0.0452911
$976$	24.0000	0.768221
$977$	−39.5147	−1.26419	−0.632094	−	0.774892i	$-0.717804\pi$
$977$	−39.5147	−1.26419	−0.632094	+	0.774892i	$0.717804\pi$
$978$	−64.7696	−2.07110
$979$	−20.4853	−0.654712
$980$	0	0
$981$	2.00000	0.0638551
$982$	−12.4853	−0.398421
$983$	1.02944	0.0328339	0.0164170	−	0.999865i	$-0.494774\pi$
$983$	1.02944	0.0328339	0.0164170	+	0.999865i	$0.494774\pi$
$984$	−19.7990	−0.631169
$985$	−10.9706	−0.349551
$986$	−11.3137	−0.360302
$987$	0	0
$988$	−2.24264	−0.0713479
$989$	−15.6569	−0.497859
$990$	−8.24264	−0.261968
$991$	48.9706	1.55560	0.777801	−	0.628511i	$-0.216335\pi$
$991$	48.9706	1.55560	0.777801	+	0.628511i	$0.216335\pi$
$992$	−2.78680	−0.0884809
$993$	−36.8284	−1.16871
$994$	0	0
$995$	4.00000	0.126809
$996$	17.1716	0.544102
$997$	−28.8284	−0.913005	−0.456503	−	0.889722i	$-0.650898\pi$
$997$	−28.8284	−0.913005	−0.456503	+	0.889722i	$0.650898\pi$
$998$	−100.326	−3.17576
$999$	48.0000	1.51865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3185.2.a.j.1.1		2
7.6	odd	2		65.2.a.b.1.1	✓	2
21.20	even	2		585.2.a.m.1.2		2
28.27	even	2		1040.2.a.j.1.2		2
35.13	even	4		325.2.b.f.274.4		4
35.27	even	4		325.2.b.f.274.1		4
35.34	odd	2		325.2.a.i.1.2		2
56.13	odd	2		4160.2.a.bf.1.2		2
56.27	even	2		4160.2.a.z.1.1		2
77.76	even	2		7865.2.a.j.1.2		2
84.83	odd	2		9360.2.a.cd.1.1		2
91.6	even	12		845.2.m.f.361.4		8
91.20	even	12		845.2.m.f.361.1		8
91.34	even	4		845.2.c.b.506.1		4
91.41	even	12		845.2.m.f.316.1		8
91.48	odd	6		845.2.e.h.146.2		4
91.55	odd	6		845.2.e.h.191.2		4
91.62	odd	6		845.2.e.c.191.1		4
91.69	odd	6		845.2.e.c.146.1		4
91.76	even	12		845.2.m.f.316.4		8
91.83	even	4		845.2.c.b.506.4		4
91.90	odd	2		845.2.a.g.1.2		2
105.62	odd	4		2925.2.c.r.2224.4		4
105.83	odd	4		2925.2.c.r.2224.1		4
105.104	even	2		2925.2.a.u.1.1		2
140.139	even	2		5200.2.a.bu.1.1		2
273.272	even	2		7605.2.a.x.1.1		2
455.454	odd	2		4225.2.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.b.1.1	✓	2	7.6	odd	2
325.2.a.i.1.2		2	35.34	odd	2
325.2.b.f.274.1		4	35.27	even	4
325.2.b.f.274.4		4	35.13	even	4
585.2.a.m.1.2		2	21.20	even	2
845.2.a.g.1.2		2	91.90	odd	2
845.2.c.b.506.1		4	91.34	even	4
845.2.c.b.506.4		4	91.83	even	4
845.2.e.c.146.1		4	91.69	odd	6
845.2.e.c.191.1		4	91.62	odd	6
845.2.e.h.146.2		4	91.48	odd	6
845.2.e.h.191.2		4	91.55	odd	6
845.2.m.f.316.1		8	91.41	even	12
845.2.m.f.316.4		8	91.76	even	12
845.2.m.f.361.1		8	91.20	even	12
845.2.m.f.361.4		8	91.6	even	12
1040.2.a.j.1.2		2	28.27	even	2
2925.2.a.u.1.1		2	105.104	even	2
2925.2.c.r.2224.1		4	105.83	odd	4
2925.2.c.r.2224.4		4	105.62	odd	4
3185.2.a.j.1.1		2	1.1	even	1	trivial
4160.2.a.z.1.1		2	56.27	even	2
4160.2.a.bf.1.2		2	56.13	odd	2
4225.2.a.r.1.1		2	455.454	odd	2
5200.2.a.bu.1.1		2	140.139	even	2
7605.2.a.x.1.1		2	273.272	even	2
7865.2.a.j.1.2		2	77.76	even	2
9360.2.a.cd.1.1		2	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3185 = 5 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3185.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.00000 q^{5} -3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.00000 q^{5} -3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} +2.41421 q^{10} +3.41421 q^{11} +5.41421 q^{12} +1.00000 q^{13} -1.41421 q^{15} +3.00000 q^{16} -0.828427 q^{17} +2.41421 q^{18} -0.585786 q^{19} -3.82843 q^{20} -8.24264 q^{22} +1.41421 q^{23} -6.24264 q^{24} +1.00000 q^{25} -2.41421 q^{26} -5.65685 q^{27} -5.65685 q^{29} +3.41421 q^{30} -1.75736 q^{31} +1.58579 q^{32} +4.82843 q^{33} +2.00000 q^{34} -3.82843 q^{36} -8.48528 q^{37} +1.41421 q^{38} +1.41421 q^{39} +4.41421 q^{40} +3.17157 q^{41} -11.0711 q^{43} +13.0711 q^{44} +1.00000 q^{45} -3.41421 q^{46} +4.82843 q^{47} +4.24264 q^{48} -2.41421 q^{50} -1.17157 q^{51} +3.82843 q^{52} +2.48528 q^{53} +13.6569 q^{54} -3.41421 q^{55} -0.828427 q^{57} +13.6569 q^{58} -1.75736 q^{59} -5.41421 q^{60} +8.00000 q^{61} +4.24264 q^{62} -9.82843 q^{64} -1.00000 q^{65} -11.6569 q^{66} -2.00000 q^{67} -3.17157 q^{68} +2.00000 q^{69} +11.8995 q^{71} +4.41421 q^{72} -8.48528 q^{73} +20.4853 q^{74} +1.41421 q^{75} -2.24264 q^{76} -3.41421 q^{78} -8.48528 q^{79} -3.00000 q^{80} -5.00000 q^{81} -7.65685 q^{82} +3.17157 q^{83} +0.828427 q^{85} +26.7279 q^{86} -8.00000 q^{87} -15.0711 q^{88} -6.00000 q^{89} -2.41421 q^{90} +5.41421 q^{92} -2.48528 q^{93} -11.6569 q^{94} +0.585786 q^{95} +2.24264 q^{96} +7.65685 q^{97} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 - 6 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} + 8 q^{12} + 2 q^{13} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} - 8 q^{22} - 4 q^{24} + 2 q^{25} - 2 q^{26} + 4 q^{30} - 12 q^{31} + 6 q^{32} + 4 q^{33} + 4 q^{34} - 2 q^{36} + 6 q^{40} + 12 q^{41} - 8 q^{43} + 12 q^{44} + 2 q^{45} - 4 q^{46} + 4 q^{47} - 2 q^{50} - 8 q^{51} + 2 q^{52} - 12 q^{53} + 16 q^{54} - 4 q^{55} + 4 q^{57} + 16 q^{58} - 12 q^{59} - 8 q^{60} + 16 q^{61} - 14 q^{64} - 2 q^{65} - 12 q^{66} - 4 q^{67} - 12 q^{68} + 4 q^{69} + 4 q^{71} + 6 q^{72} + 24 q^{74} + 4 q^{76} - 4 q^{78} - 6 q^{80} - 10 q^{81} - 4 q^{82} + 12 q^{83} - 4 q^{85} + 28 q^{86} - 16 q^{87} - 16 q^{88} - 12 q^{89} - 2 q^{90} + 8 q^{92} + 12 q^{93} - 12 q^{94} + 4 q^{95} - 4 q^{96} + 4 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 - 6 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^11 + 8 * q^12 + 2 * q^13 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 - 8 * q^22 - 4 * q^24 + 2 * q^25 - 2 * q^26 + 4 * q^30 - 12 * q^31 + 6 * q^32 + 4 * q^33 + 4 * q^34 - 2 * q^36 + 6 * q^40 + 12 * q^41 - 8 * q^43 + 12 * q^44 + 2 * q^45 - 4 * q^46 + 4 * q^47 - 2 * q^50 - 8 * q^51 + 2 * q^52 - 12 * q^53 + 16 * q^54 - 4 * q^55 + 4 * q^57 + 16 * q^58 - 12 * q^59 - 8 * q^60 + 16 * q^61 - 14 * q^64 - 2 * q^65 - 12 * q^66 - 4 * q^67 - 12 * q^68 + 4 * q^69 + 4 * q^71 + 6 * q^72 + 24 * q^74 + 4 * q^76 - 4 * q^78 - 6 * q^80 - 10 * q^81 - 4 * q^82 + 12 * q^83 - 4 * q^85 + 28 * q^86 - 16 * q^87 - 16 * q^88 - 12 * q^89 - 2 * q^90 + 8 * q^92 + 12 * q^93 - 12 * q^94 + 4 * q^95 - 4 * q^96 + 4 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more